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Simplifying
(5m + 4n)(5m + -4n) = 0
Multiply (5m + 4n) * (5m + -4n)
(5m * (5m + -4n) + 4n * (5m + -4n)) = 0
((5m * 5m + -4n * 5m) + 4n * (5m + -4n)) = 0
Reorder the terms:
((-20mn + 25m2) + 4n * (5m + -4n)) = 0
((-20mn + 25m2) + 4n * (5m + -4n)) = 0
(-20mn + 25m2 + (5m * 4n + -4n * 4n)) = 0
(-20mn + 25m2 + (20mn + -16n2)) = 0
Reorder the terms:
(-20mn + 20mn + 25m2 + -16n2) = 0
Combine like terms: -20mn + 20mn = 0
(0 + 25m2 + -16n2) = 0
(25m2 + -16n2) = 0
Solving
25m2 + -16n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '16n2' to each side of the equation.
25m2 + -16n2 + 16n2 = 0 + 16n2
Combine like terms: -16n2 + 16n2 = 0
25m2 + 0 = 0 + 16n2
25m2 = 0 + 16n2
Remove the zero:
25m2 = 16n2
Divide each side by '25'.
m2 = 0.64n2
Simplifying
m2 = 0.64n2
Take the square root of each side:
m = {-0.8n, 0.8n}
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